1. A drum of kerosene oil is \( \frac{3}{4} \) full. When 15 litres of oil is drawn from it, it is \( \frac{7}{12} \) full. Find the total capacity of the drum.
\[ \begin{align*} \text{Let total capacity of drum} & = x \text{ litres} \\ \\ \text{Oil in the drum} & = \frac{3x}{4} \\ \\ \text{Oil drawn out} & = 15 \text{ litres} \\ \\ \text{Remaining oil in the drum} & = \frac{7x}{12} \\ \\ \frac{3x}{4} -15 & = \frac{7x}{4} \\ \\ \frac{3x}{4} -\frac{7x}{12} & = 15 \\ \\ \frac{9x - 7x}{12} & = 15 \\ \\ \frac{\cancelto{1}{2}x}{\cancelto{6}{12}} & = 15 \\ \\ \frac{x}{6} & = 15 \\ \\ x & = 15 \times 5 \\ \\ x & = 90 \text{ litres}\\ \\ \end{align*} \]
Answer Total capacity of the drum \( \boxed{\color{red}90 \text{ litres}} \).
2. \( \left(1 - \frac{1}{2} \right) \left(1 - \frac{1}{3} \right) \left(1 - \frac{1}{4} \right)...\left(1 - \frac{1}{10} \right) \)
\[ \begin{align*} &= \left(\frac{1}{1} - \frac{1}{2} \right) \left(\frac{1}{1} - \frac{1}{3} \right) \left(\frac{1}{1} - \frac{1}{4} \right)...\left(\frac{1}{1} - \frac{1}{10} \right) \\ \\ &= \left(\frac{2 - 1}{2} \right) \left(\frac{3 - 1}{3} \right) \left(\frac{4 - 1}{4} \right)...\left(\frac{10 - 1}{10} \right) \\ \\ &= \left(\frac{1}{2} \right) \left(\frac{2}{3} \right) \left(\frac{3}{4} \right)...\left(\frac{9}{10} \right) \\ \\ &= \frac{1}{\cancelto{1}{2}} \times\frac{\cancelto{1}{2}}{\cancelto{1}{3}} \times \frac{\cancelto{1}{3}}{\cancelto{1}{4}} \times \frac{\cancelto{1}{4}}{\cancelto{1}{5}} \times \frac{\cancelto{1}{5}}{\cancelto{1}{6}} \times \frac{\cancelto{1}{6}}{\cancelto{1}{7}} \times\frac{\cancelto{1}{7}}{\cancelto{1}{8}} \times \frac{\cancelto{1}{8}}{\cancelto{1}{9}} \times\frac{\cancelto{1}{9}}{10} \\ \\ &=\frac{1}{10} \\ \end{align*} \]
Answer \( \boxed{\color{red}\frac{1}{10}} \)